Quantum-like World of Cancer Complexity
Cancer is a heterogeneous disease. Even the single cancer type can be divided into a multitude of varieties. Each of them significantly affects prognosis and treatment options (1).
For instance, breast cancer is actually a collection of at least 12 unique biological groups (2). And these 12 groups exist only when considering so-called “intertumoural heterogeneity”, based on genomic profiling of the dominant cancer cell population.
If we delve deeper and analyse a tumour at the single-cell resolution, we will discover another layer of diversity among tumour cell subpopulations – “intratumoural heterogeneity”. There, we will face different densities of blood and lymphatic vasculature, different compositions of extracellular matrix, different cancer cell types (e.g. differentiated cancer cells, cancer stem cells, cancer-associated fibroblasts, tumour-associated macrophages) and their different relative number and spatial organization.
Each of these cell types has different migration and invasion capabilities, proliferation, and stemness levels. What is more troubling is that these cells are highly plastic; i.e., they have the ability to rapidly react to changes in their surrounding by changing their metabolism, morphology, migration and proliferation rate. Therefore, only a part of the differences between cell types stems from the intrinsic properties of cells. An equally large part of variability is a result of complex interactions between cells and the extracellular matrix.
Where are we in understanding tumour complexity
Do we currently understand this complexity? No. We only scratched the surface of discovering the interplay of various genetic, epigenetic and regulatory factors. Trying to experimentally untangle it will, unfortunately, take a very long time as
“more sophisticated combinations of genomic, epigenomic, transcriptomic and proteomic analyses at the single-cell level will be required to further delineate the functional implications of tumour heterogeneity during the metastatic process” (3).
And even when (if?) we finally enlist all the details of metabolic regulations and their physiological consequences, it is not obvious that it will directly lead to an actionable treatment guideline. More probably we will spend additional decades trying to determine the size of the effect of tweaking those intertwined regulatory factors with drugs.
The elusive “Data” holy grail
Whether we will ever reach the holy grail of having all the data to ‘precisely enough’ predict the outcome of our intervention, is, at best, highly questionable.
As our understanding of cancer biology progresses, the set of known factors that influence its behaviour, and ultimately the clinical outcome, is becoming bigger and bigger. With that, we are marching towards an ever-increasing universe of parameters with progressively more complex rules, that will soon be almost impossible to fully comprehend. These parameters can easily expand beyond human cell physiology. For instance, some of the well-documented cases of spontaneous remission cases show strong correlations with bacterial and viral infections (4). Indeed, the most probable mechanism of the anti-tumour effect in these cases is the specific activation of the immune response triggered by an infection. However, to control that, we will need a much better understanding of our immune system functioning, than we currently have. This leads us further down the ‘gathering all the data’ rabbit hole, which, at this point, seems endless.
Does quantum mechanics give us a better way to approach cancer biology?
So, what could we do? Increased knowledge of minute biological details indeed led to the development of novel treatments. However, most of the reduction in cancer deaths is not even related to novel treatments (see for example 5). Therefore, in parallel to those immensely important experimental efforts, we should try to understand the probabilistic behaviour of such fluid and changeable systems, as tumours are.
As chance would have it – the basic mathematical framework for that has already been developed in the quantum mechanics field.
Namely, very similiar problems of measurement uncertainty and contextuality have long hauled the world of quantum dynamics.
What initially started as an attempt to understand the behaviour of atoms and elementary particles, soon transformed into a well-formalized set of rules for calculating probabilities of certain observable properties.
What Werner Heisenberg realized early enough is that even if we do not know the underlying mechanisms that govern the behaviour of a system, we could non-the-less build a powerful mathematical framework for predicting the behaviour of a said system, based on relationships between observable quantities. At the same time, having those calculation rules did not preclude theoretical discussion on the role of “hidden variables” and whether they even exist.
So, quantum mechanics embraced the lack of “understanding” and continued its march towards better knowledge in a very pragmatic way – by combining a powerful mathematical approach (which assumes there is nothing underlying the observed phenomena) with theoretical and experimental work towards the depth of the quantum world (which assumes there is much behind the observations).
How can this be used in cancer biology? In the last 10 years several powerful, generalized mathematical approaches have been developed, inspired by quantum mechanic problems. For instance, Samson Abramsky and Adam Brandenburger developed a generalized mathematical treatment of contextuality using category theory (6). On the other hand, Acin et al. used hypergraphs to deal with a similar set of problems. (7). Both, category theory and graph theory are general enough that they provide a unifying common language for the structure of mathematical objects (category theory) and the inner working of complex systems (graph theory). So, findings proved to be true in these generalized approaches, can be relatively easily “scaled-down” to a particular object in question…in this case a tumour. Without implying that tumours share any of the much-discussed properties of quantum systems (nonlocality, fundamental indeterminism), we believe that systemic dealing with their uncertainty is a way forward in understanding the behaviour of tumours. It will maybe not help us in understanding underlying biology, but will certainly lead towards drawing a more comprehensive outline of its clinical behaviour. For that, we should borrow and adapt mathematical tools that already exist.